Chris invests $12,000 in an account. The interest is compounded monthly at an annual rate of 11.6%. The ending account balance will be $33,916.21. How many years was the investment accruing interest?
--use a TVM calculator
i = .116/12 = .0096666...
n = ? , where n is in months.
12000(1.009666..)^n = 33916.21
(1.009666...)^n = 2.82635...
take log of both sides, applying standard log rules:
n log 1.0096666... = lof 2.82635..
n = 108 correct to 5 decimal places
108 months = 9 years
To find out how many years the investment was accruing interest, we can use a Time Value of Money (TVM) calculator. The TVM formula we will be using is:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = Future Value ($33,916.21 in this case)
PV = Present Value ($12,000)
r = Annual interest rate (11.6%)
n = Number of compounding periods per year (12, since the interest is compounded monthly)
t = Number of years (unknown)
Rearranging the formula to solve for t, we get:
t = (log(FV/PV)) / (n * log(1 + r/n))
Now we can substitute the given values into the equation:
t = (log(33,916.21/12,000)) / (12 * log(1 + 0.116/12))
Using a TVM calculator, we get:
t ≈ 9.011
Therefore, the investment was accruing interest for approximately 9.011 years.